# How do I use a free body diagram in this case?

• EddiePhys
In summary, the conversation discusses two cases where the acceleration of m1 needs to be calculated. The first case involves considering m1 and m2 as a system, while the second case involves using a free-body diagram. In the second case, it is noted that m2 affects the vertical motion but not the horizontal acceleration due to the frictionless surfaces. The conversation also touches on the possibility of the support arm holding m2 influencing the acceleration, and the use of a free-body diagram to determine the distribution of force between m1 and m2.

#### EddiePhys

In the above cases I want to find the acceleration a for m1. I can do it by considering m1 and m2 to be a system, which would give me a = F/(m1+m2). How can I use a free-body diagram instead to calculate the acceleration? Using a free-body diagram, m2 only affects the vertical motion by exerting a vertical force and not the horizontal acceleration but we know that since the mass of the system has increased the acceleration will decrease. TLDR; how would I solve for the acceleration of m1 in both of the above cases using only a free-body diagram. All surfaces are frictionless.

EddiePhys said:
Using a free-body diagram, m2 only affects the vertical motion by exerting a vertical force and not the horizontal acceleration

In the first diagram, is the support arm holding m2 rigid, and rigidly attached to m1? It might make things more clear if you consider the support arm as a third object with a very small mass.

In the second diagram, if the contact between m1 and m2 is indeed frictionless, what should you expect to happen, intuitively, when you push on m1 (alone)? Have you ever pushed one object out from underneath another one that is resting on top of it?

jtbell said:
In the first diagram, is the support arm holding m2 rigid, and rigidly attached to m1? It might make things more clear if you consider the support arm as a third object with a very small mass.

In the second diagram, if the contact between m1 and m2 is indeed frictionless, what should you expect to happen, intuitively, when you push on m1 (alone)? Have you ever pushed one object out from underneath another one that is resting on top of it?

1) Yes, it's holding m2 in place
2) Yes, it would slide from beneath m2, but for the time m2 is on top of m1, wouldn't it affect the acceleration?

Could you please show me how to make a free-body diagram in the two cases such that the horizontal acceleration is affected too?

For 2) above, no it would not affect the acceleration of m1 because there is no friction so no force.

I'm not sure what you're getting at with your question. My best guess is you want to figure out how much of F is going to accelerate m1 and how much is going to accelerate m2. You can't do that with a free-body diagram in this case.

## 1. What is a free body diagram and why is it important in science?

A free body diagram is a visual representation of the forces acting on an object. It is important in science because it helps us understand and analyze the motion of objects by identifying the different forces at play.

## 2. How do I create a free body diagram for a given scenario?

To create a free body diagram, you must first identify the object or system of objects you want to analyze. Then, draw a simple sketch of the object(s) and label all the forces acting on it. Finally, use arrows to represent the magnitude and direction of each force.

## 3. Can I use a free body diagram for both stationary and moving objects?

Yes, a free body diagram can be used for any object, whether it is stationary or in motion. It is particularly useful for analyzing the forces acting on an object at different points in its motion.

## 4. How does a free body diagram help in problem-solving?

A free body diagram helps in problem-solving by providing a visual representation of the forces acting on an object. This allows us to accurately calculate the net force and acceleration of the object, which are crucial in solving equations of motion.

## 5. Are there any tips or tricks for using a free body diagram effectively?

One important tip for using a free body diagram effectively is to always include all the forces that are acting on the object, even if they cancel each other out. Also, it is helpful to use a scale and choose a consistent direction for all the forces, such as positive and negative directions along an axis.